Method and system for reducing intra-channel nonlinear effects in highly dispersed optical pulse transmission

ABSTRACT

A system and-method for reducing timing and amplitude jitter in transmission of Retrun-to-Zero modulated pulses is described. In the reduction of amplitude jitter the modulated pulses must be phase coherent. The method comprises the steps of measuring a total dispersion of a transmission fiber link, computing an optimal amount of pre-chirp to be added at an input of said transmission fiber link, computing an optimal amount of pre-chirp to be added at an output of said transmission fiber link, adding said optimal amount of pre-chirp to said input of said transmission fiber link and adding said optimal amount of pre-chirp to said output of said transmission fiber link. The system for reducing timing jitter in transmission of Return-to-Zero modulated pulses comprises means for measuring a total dispersion of a transmission fiber link, means for computing an optimal amount of pre-chirp to be-added at an input of said transmission fiber link, means for computing an optimal amount of pre-chirp to be added at an output of said transmission fiber link, means for adding said optimal amount of pre-chirp to said input of said transmission fiber link and means for adding said optimal amount of pre-chirp to said output of said transmission fiber link.

This application claims the benefit of priority of ProvisionalApplication No. 60/219,355, filed on Jul. 19, 2000, and of ProvisionalApplication No. 60/267,724, filed on Feb. 12, 2001.

FIELD OF THE INVENTION

The present invention relates to the field of optical communicationssystems and particularly to a method for reduction or elimination oftiming jitter and amplitude jitter occurring in transmission ofReturn-to-Zero (RZ) modulated pulses by use of optimum amount ofpre-chirp.

BACKGROUND OF THE INVENTION

Transmission of optical pulses based on RZ modulation is emerging as thebest choice in high bit rate and/or long distance systems. However, thepulses suffer from nonlinear intra-channel effects, which lead to timingjitter and amplitude jitter. Timimg jitter and amplitude jitter weakenthe performance and limit the maximum capacity of each channel.

SUMMARY OF THE INVENTION

Dispersion describes how a signal is distorted due to the variousfrequency components of the signal having different propagationcharacteristics. Specifically, dispersion is the degree of scattering inthe light beam as it travels along a fiber span. Dispersion can also becaused by the frequency dependence of the group velocity of a lightsignal propagating inside a fiber.

The intricate interplay of nonlinearity and dispersion acting on pulsesin optical fibers continues to challenge the conventional wisdom andestablished intuition. One example is the idea that short duty-cycle RZtransmission in dispersive fibers is able to combat the detrimentaleffects of fiber nonlinearity. Due to their short width, the pulsesdisperse rapidly, spreading in time over hundreds or thousands of bits.Theory, simulations and experiments in the prior art uniformly show thatwith shorter pulses the nonlinear impairments are reduced. This may seemsomewhat counter-intuitive since the reduction of the pulse width isinevitably accompanied by an increase in the pulse peak power and anincrease in the impact of self-phase modulation (SPM) may be expected.SPM causes compression in the pulse. The reason for the reduction is notmerely that the individual peak power is reduced by dispersion. In arandom bit sequence the intensity pattern of the interfering pulsescontains spikes that are of the same order of magnitude as the inputpeak power. The reduced peak power is, therefore, not a viableexplanation. Rather, the mechanism for the tolerance towards nonlinearimpairments relies on the fact that the intensity pattern changes veryrapidly. Thus, the accumulated effect of the instantaneous nonlinearitytends to get averaged out and SPM and nonlinear pulse interaction isreduced even though the pulses spread over hundreads of neighboring timeslots. The concept of spreading the pulses as far as possible and asquickly as possible in the time domain, creating a rapidly varyingintensity pattern, in order to combat the impact of nonlinearity,represent such a big shift from standard dispersion managed approachesthat a specific term “tedon-transmission” has been coined to representthis scheme.

System penalties are generated in the form of timing and amplitudejitter, which limit the performance of such systems. It may be useful tonote that the scheme presented herein is fundamentally different fromschemes, which rely on soliton transmission where the pulses usually donot spread over more than tens of bits.

Analysis of the nonlinear pulse interaction in systems based on highlydispersed optical pulses provides estimates of timing and amplitudejitter. The pulse streams are both coherent and non-coherent. Analysisof the nonlinear intra-channel effects indicate that the non-lineareffects possess a symmetry when pre-chirped pulses are launched. Systempenalties reduce montonically with decreasing pulse width and withincreasing fiber dispersion. Proper dispersion pre-compensation canresult in a significant reduction of the nonlinear impairments. Optimalpre-compensation can be determined analytically.

It is, therefore, an object of the present invention to minimize timingjitter by injecting the proper amount of pre-chirp into thecommunications link.

A further object of the present invention is to minimize amplitudejitter by injecting the proper amount of pre-chirp into thecommunications link.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is best described with reference to the detaileddescription and the following figures, where:

FIG. 1a shows the timing jitter as a function of position along the linkwith 4 dBm average input power.

FIG. 1b shows the effect of pre-compensation on timing jitter at thelink output for average input powers of 4 dBm, 7 dBm and 10 dBm.

FIG. 1c shows the amplitude jitter at the link output as a function ofthe pre-compensation parameter with the average input powers of 4 dBmand 7 dBm.

FIG. 1d shows the mean energy in the time slots corresponding to logicalzeroes for average input powers of 4 dBm and 7 dBm.

FIG. 2 (top) illustrates timing jitter versus link length and (bottom)shows eye diagrams captured at points marked in the top of the figure.

FIG. 3 is a simple flowchart of the steps to reduce timing and amplitudejitter.

FIG. 4 is a simple block diagram of an exemplary implementation of asystem for reducing or eliminating timing and amplitude jitter.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention concentrates on timing and amplitude jitter aswell as the energy of pulses generated in time slots corresponding tological zeroes. Analytical estimates of timing and amplitude jitter insystems based on highly dispersed optical pulses can be obtained. Systempenalties reduce monotonically with decreasing pulse width and withincreasing chromatic dispersion. There is a qualitative differencebetween the phase coherent case, when there is a fixed relationship withthe pulse stream, and the incoherent case, where the phase relationbetween pulses is random. The two cases are equivalent in terms of thetiming jitter but differ significantly in terms of the amplitude jitterand the noise of the zeroes. In the coherent case there is a largernoise on zeroes but the amplitude jitter can be minimized byquasi-symmetric dispersion compensation. In the incoherent case, thenoise on zeroes is lower but no improvement in the amplitude jitter canbe obtained by manipulating the dispersion compensation scheme.

In the case of RZ modulation with Gaussian shaped pulses propagating ina sequence of lossy, dispersive fiber spans with periodic amplificationand further assuming highly dispesive pulses for 40 Gbits/s over 800 kmconventional single mode fiber, where the dispersion compensation isapplied at the receiver as opposed to span by span the expressions fortiming and amplitude jitter can be derived. The derivations of theexpressions for the timing and amplitude jitter rely only on theassumptions that are inherent to the perturbational approach. Assuming arandom sequence of Gaussian shaped pulses at the system input${\sum\limits_{n = {- \infty}}^{\infty}{m_{n}{u_{n}\left( {0,t} \right)}}},$

where m_(n) is equal to 0 or 1 with probability of 0.5, and whereu_(n)(0,t)=A₀ exp(−0.5(t-nT)²/τ²) with T=1/B, B being the data rate andaveraging over all possible two-pulse interactions yields the followingresult:

std(t ₁)B=C ₁ γP _(av)τ^(3/2) √{square root over (B/|B₂|)}  (1)

where std(td) denotes the standard deviation of the temporal pulseposition, defined as the position of the center of mass of the pulset₁=(1/E₁)∫t|u_(n)(L,t)|²dt, E₁=√{square root over (π)}A₀ ²τ is theenergy of the pulses, P_(av)=E₁B/2 is the average power of the signal, γis the nonlinearity coefficient, τ is the full width at half maximum ofthe pulse and B₂ is the dispersion coefficient. Because of thelinearization approximation, and of the large number of pulsesinteracting with any given one, the temporal pulse position is alsofound to be Gaussian distributed. The term C₁, which is a cumbersomefunction of both the chirp parameter of the injected pulses and of thefiber loss coefficient, is a proportionality coefficient given by:$\begin{matrix}{{C_{1}^{2} = {\frac{2\sqrt{2}}{\sqrt{\pi}}I_{1}}}{where}{I_{1} = {\int_{- z^{*}}^{L - z^{*}}{{z}{\int_{- z^{*}}^{L - z^{*}}{{z^{\prime}}\frac{z\quad {f\left( {z + z^{*}} \right)}z^{\prime}{f\left( {z^{\prime} + z^{*}} \right)}}{\left( {z^{2} + z^{\prime 2}} \right)^{3/2}}}}}}}} & (2)\end{matrix}$

f(z) is the ratio of the average power at z and the power at the inputof the line and L is the link length. The term z* denotes the portion ofthe fiber length whose dispersion is pre-compensated for at thetransmitter side. The reason for including only two pulse interactionsin the averaging that led to equation (1) is that, as shown in the priorart, only cross phase modulation contributes to timing jitter; Ananalytical expression for C₁ can be obtained in the simplified case of alossless fiber, where f(z)=1 so that C₁ ²=2√{square root over(2/π)}[2√{square root over ((L−z*)²)}+z^(*2) −√{square root over(2)}(|L−z*|+|z*|)].This expression can be used in equation (1) afterreplacing P_(av) with the path averaged optical power to obtain anorder-of-magnitude estimate of the timing jitter. This suggests that thegrowth of the timing jitter is approximately proportional to the squareroot of the length of the link. Note the strong dependence of timingjitter on the launched pulse width, which stresses the advantage ofusing short pulses. Additionally, the dependence on the dispersioncoefficient exposes the advantage of-high dispersion fibers in thistransmission scheme. That is, in order to minimize the timing jitter,the optimum amount of pre-chirp is found by means of minimizing, byvariation of z*, the integral I₁, which is defined above.

Since timing jitter is generated by cross-phase modulation, which is anincoherent process, equations (1) and (2) hold regardless of the phaserelationship between the transmitted pulses. In order to analyzeintensity impairments the cases of phase coherence and phase incoherenceneed to be explicitly separated. The phase coherent case occurs when thepulses originate from a single mode locked laser or from a continuouswave (CW) laser whose intensity is externally modulated. This applies tomost cases of electrical time-division multiplexing (ETDM). The phaseincoherent case prevails typically when the launched pulse streamoriginates from more than one source laser as in the case of opticaltime-division multiplexing (OTDM).

In the case of phase coherence, equally spaced pulses have an equalphase difference between them. The standard deviation of the pulseenergy divided by the mean energy of ones, which are referred to asamplitude jitter, is obtained from the following expression:$\begin{matrix}{{\frac{s\quad t\quad {d\left( E_{1} \right)}}{E_{1}} = {C_{2}\gamma \quad P_{av}\tau}},} & (3)\end{matrix}$

where C₂ is a proportionality coefficient depending only on B, z* andthe fiber parameters and not on the average power P_(av) nor on thepulse width τ. The proportionality coefficient may be obtained as anaverage over the tranmsitted message of all three pulse interactionsyielding a cumbersome expression. An appropriate expression can beobtained in the asymptotic case where |B₂|LB²>>1, yielding$\begin{matrix}{{{C_{2}^{2} \cong {\frac{8\quad {\log \left( {{B_{2}}L\quad B^{2}} \right)}}{3{B_{2}}}I_{2}}},{where}}{I_{2} = {{\int_{0}^{L}{{z}\quad f\quad (z)^{2}}} - {\int_{- z^{*}}^{L - z^{*}}{{z}\quad {f_{w}\left( {z + z^{*}} \right)}{f_{w}\left( {{- z} + z^{*}} \right)}}}}}} & (4)\end{matrix}$

and f_(w)(z)=f(z)rect(z;0,L), with rect(z;0, L) being a function whichis 1 for 0≦z≦L and zero elsewhere. The approximation leading to equation(4) involves the disregard of the correlation between contributions ofdifferent three pulse interactions to amplitude jitter. This disregardis justified by the large number of interacting pulses in this scheme.Similarly to the timing jitter, the amplitude jitter decreases withincreasing dispersion or decreasing pulse width. Its dependence on pulsewidth is, however, more moderate. The approximate expression for C₂allows for optimization of the pre-compensation parameter z* for theminimization of the amplitude jitter.

That is, in order to minimize the amplitude jitter, the optimum amountof pre-chirp is found by means of minimizing, by variation of z*, theintegral I₂, which is defined above.

The minimization of these integrals (I₁ and I₂) can be performedaccurately and quickly with standard numerical techniques. Heuristic,simplifying approximations are also available. It is beneficial to useany amount of pre-chirp in a range around the optimum amount. In systemswith symmetric power evolutions, the optimum amount of pre-chirp isclose to half of the total dispersion in the link. Since, however, itmay be shown by numerical evaluations of I₁ and I₂ that I₂ is moresensitive to the amount of pre-chirp and that with the amount ofpre-chirp that minimizes I₂ the quantity I₁ is also very close to itsminimum value, the optimization of the link for that concerns bothamplitude and timing jitter is performed by using the amount ofpre-chirp that minimizes I₂.

In the particular case of a link made of n lossy fiber segments oflength z₀(L=nz₀)and lumped amplification with Erbium amplifiers, theprocedure of the present invention can be followed analytically. In thiscase, f(z)=exp[−αmod(z,z₀)], where α is the fiber loss coefficient andmod(z,zo) is the remainder of the division of z by z₀, and the minimumvalue for C₂ is obtained for $\begin{matrix}{z_{opt}^{*} = {\frac{n\quad z_{0}}{2} - {\frac{{n\left( {{\alpha \quad z_{0}} - 1} \right)} + {\left( {n - 1} \right){\exp \left( {{- \alpha}\quad z_{0}} \right)}}}{2\quad {\alpha \quad\left\lbrack {n - {\left( {n - 1} \right){\exp \left( {{- \alpha}\quad z_{0}} \right)}}} \right\rbrack}}.}}} & (5)\end{matrix}$

For the above expression to be valid, z*_(opt)≦(nz₀)/2 should beconsistently verified that it is large enough and that αz₀ is realistic.The point of zero accumulation dispersion z*_(opt) always precedes thecenter of the line by less than half a span length. An evaluation of C₁shows that the timing jitter for z*=z*_(opt) is also very close to itsminimum.

Similarly, the mean energy of the echo pulses appearing in the timeslots corresponding to logical zeroes (in the phase coherent case) canbe expressed as $\begin{matrix}{{\frac{{mean}\left( E_{0} \right)}{E_{1}} = {\left( {C_{3} + C_{4}} \right)\gamma^{2}P_{av}^{2}\tau^{2}}},} & (6)\end{matrix}$

where once again the terms C₃ and C₄ are proportionality coefficientsdepending only on B, z* and the fiber dispersion parameters. Using thesame approximations as in the derivation of (6) in the asymptotic regime|B₂|LB²>>1, C₃ and C₄ are given by${C_{3} \cong {\frac{\pi \quad \sqrt{3}}{12}{B^{2}\left\lbrack {\int_{0}^{L}{{z}\quad {f(z)}}} \right\rbrack}^{2}}},{C_{4} \cong {\frac{4\quad {\log \left( {{B_{2}}L\quad B^{2}} \right)}}{\sqrt{3}{B_{2}}}{\int_{0}^{L}{{z}\quad {{f(z)}^{2}.}}}}}$

The power of the echo pulses is independent, within the variability ofthe approximations, of the pre-compensation, z*, whereas both timing andampitude jitter strongly depend on it.

In the phase incoherent case in which the phase of the transmittedpulses is random, there is a random phase relation between thecontribution of the nonlinear interaction and the transmitted pulse at agiven time slot. A general relation between the amplitude jitter and theaverage power of the echo pulses at the position where a logical zero istransmitted is found as follows: $\begin{matrix}{\frac{s\quad t\quad {d\left( E_{1} \right)}}{E_{1}} = {{\sqrt{\frac{2}{\sqrt{3}}}\left\lbrack \frac{{mean}\left( E_{0} \right)}{E_{1}} \right\rbrack}.}} & (9)\end{matrix}$

Asymptotically, for |B₂|LB²>>1, the energy of the echo pulses is stilldescribed by equation (6), only with C₃=0, as certain phase sensitivecontributions are averaged out. Since C₃>0 this implies that the energyof the echo pulses at zeroes is always smaller in the phase incoherentcase. To understand the amplitude jitter of ones, equation (6) with C₃=0can be inserted into equation (9) which shows that the amplitude jitteris given exactly by equations (3) and (4), only without the secondintegral in the square brackets of equation (4). Since the value of thisintegral is always non-negative the amplitude jitter in the incoherentcase is equal to or larger than in the case of phase coherent pulses.Based on the above, the pre-compensation of the signal in the incoherentcase has no effect either on the amplitude jitter or on the averageenergy of zeroes.

To confirm the theoretical results a comprehensive series of simulationshave been performed and are presented herein using a 40 Gb/s PseudoRandom Bit Sequence (PRBS) consisting of 2.5 ps wide Gaussian shapedpulses is injected into 10×80 km spans of standard single mode fiber(SMF) with B₂=−21.67 ps²/km, γ=1.2 W⁻¹ km⁻¹ and α=0.048 km⁻¹. Thesimulations were performed with a time window equivalent to 2048symbols. This large time window was necessary, since with the parametersthe number of overlapping pulses was as large as 1500. Other simulationsusing a shorter time frame consisting only of 512 symbols led todeviations on the order of 30% in the computation of the timing jitter.FIG. 1a shows the timing jitter as a function of position along the linkwith 4 dBm average input power. Both the theoretical expression (1) andthe simulation results are displayed for two values of pre-compensationz*=0 and z*=z*_(opt)=370 km. There is a noticeable large advantage ofoptimal pre-compensation, leading to a reduction by a factor of 4.55 inthe resulting timing jitter. The effect of pre-compensation on timingjitter at the link output is shown in FIG. 1b for average input powersof 4 dBm, 7 dBm and 10 dBm. The results are normalized to the averagelaunched power. The fact that the points obtained with the three powersnearly overlap in the figure confirms the validity of the pertubationalapproach up to these powers. The amplitude jitter at the link output isshown as a function of the pre-compensation parameter in FIG. 1c withthe average input powers of 4 dBm and 7 dBm. The theoretical predictionfor z*_(opt) in the coherent case is in agreement with the simulationresults. In the incoherent case there is a larger amplitude jitter andits value is practically independent of the pre-compensation parameter.The mean energy in the time slots corresponding to logical zeroes foraverage input powers of 4 dBm and 7 dBm is plotted in FIG. 1d. Itsdependence on the value of pre-compensation is negligible as expected,and its value is smaller in the incoherent case.

The effect of pre-dispersion, which is at the root of the presentinvention, is most clearly observed and understood when the powerprofile along the fiber is symmetric about the center of the link. Thissymmetry can be obtained, at least approximately, by introducing Ramanamplification with a counter-propagating pump (or pumps). In such casesboth the timing and amplitude jitter can be canceled out by equallysplitting the dispersion compensation between the input and output ofthe optical link, as it can be shown that both I₁ and I₂ are zero forz*=z*_(opt)=L/2. It has been shown that the present invention, however,permits, optimization of the amount of predispersion to yield asignificant reduction of the transmission penalties in more realisticcases when the power profile is not perfectly symmetric.

To demonstrate this effect FIG. 2 shows three different sets ofsimulations, where we used 4 ps pulses with an average power of 7 dBm.In the top figure only the timing jitter is plotted against the linklength. The amplitude jitter has a similar evolution. The triangles showthe timing jitter in a lossy link with Raman amplified fiber spans of 80km, and without pre-dispersion. The Raman pump power was chosen suchthat the fiber losses were compensated in each span. The asterisks showthe timing jitter for the same link, but where the pulses arepre-dispersed by −2720 ps/nm. In this case, the pulses aretransform-limited at 160 km where the penalties are maximal and after320 km the penalties are minimized. The circles demonstrate the exactcancellation of the timing jitter in a lossless fiber link and afterpre-dispersion by 2720 ps/nm. The power in the lossless case was set tothe average power in the Raman amplified cases.

In the three cases eye-diagrams have been detected at 320 km. These areindicated in FIG. 2 (at points marked 1-3). It is clear that thepenalties are eliminated in the ideal lossless case and that thepenalties in the Raman amplified link are reduced because of thepre-dispersion.

The simulations presented in FIG. 2 herein assumed a single Raman pump.Multiple pumps can, in principle, further improve the symmetry of thelink so that better cancellation of the penalties can be expected. Notethe similarity with the cancellation of the impairments due to opticalnonlineadties obtained by mid-span spectral inversion. Both require asymmetric power profile. It is, however, surprising that in the presentcase this result is obtained only by a proper dispersion management ofthe link.

Analytical formulae, simulations and a method for overcoming timing andamplitude jitter in systems based on ultra short pulse transmission havebeen presented. Additionally, it has been shown that the systempenalties reduce monotonically with increasing fiber dispersion as wellas with decreasing pulse width. Further, it has been shown that thecombination of counterpropagating Raman amplification and properpredispersion of the optical pulses enables a significant reduction ofthe impairments. The method works equally well without Raman amplifier,permitting the reduction of timing and amplitude jitter also when lumpedamplification with Erbium amplifiers is used.

In summary, nonlinear impairments due to intrachannel interactions inschemes involving ultrashort pulse (tedon) transmission with random bitsequences have been studied. The amount of timing jitter, amplitudejitter of logical ones and the mean noise on the level of logical zeroeshave been presented. The analysis shows the advantage of using shortpulse widths and fibers with large chromatic dispersion. It has beenfurther shown that optimal pre-compensation allows significant reductionof timing and amplitude jitter in phase coherent cases.

FIG. 3 is a simple flowchart of the steps to follow to reduce oreliminate timing and amplitude jitter. Means for measuring totaldispersion of a transmission fiber link and are known in the art.Computing devices including processors and system as well as ApplicationSpecific Integrated Circuits (ASICs), Field programmbale Gate Arrays(FPGAs), Reduced Instruction Set Computers (RISCs), or any combinationthereof or any similar device designed for performing the computationsspecified herein, can be used to implement the compuation of the optimalpre-chirp and therefore, provides a means for performing thecomputation. The specified computation of optimal pre-chirp may even becomputed using a high-end pocket calculator or computer. Two devices areused, one at the input of the transmission fiber and the other at theoutput of the transmission fiber. Dispersion is added to the signalopposite in sign to the dispersion of the transmission fiber. The twodevices may be fibers; gratings or any other device used for thispurpose. The two devices for dispersion compensation should, however, bedesigned such that the device at the input adds dispersion −z*_(opt)B₂and the device at the output adds −(1−z*_(opt))B₂, where B₂ is the totaldispersion of the link.

FIG. 4 represents a simple block diagram of an exemplary implementationof a system to reduce or eliminate timing and amplitude jitter. The boxto the far left with a “T” represent a transmitter. The trnasmissionfiber, which may have a plurality of in-line amplifiers, is represent bythe letters “TF”. The box to the far right with the letter “R”represents the receiver. The dispersion compensation devices arerepresented by “(a)” and “(b)”, with “(a)” being the dispersioncompensation device at the input of the transmission fiber and with“(b)” being the dispersion compensating device at the output of thetransmission fiber. The amounts of dispersion to be added to the inputand the output of the tranmission fiber is as specified above in thedescription of FIG. 3.

The present invention may be implemented in hardware, software orfirmware as well as Application Specific Integrated Circuits (ASICs) orField Programmable Gate Arrays (FPGAs) or any other menas by which thefunctions and process disclosed herein can be effectively andefficiently accomplished or any combination thereof. The above means forimplementation should not be taken to be exhaustive but merely exemplaryand therefore, not limit the means by which the present invention may bepracticed.

It should be clear from the foregoing that the objectives of theinvention have been met. While particular embodiments of the presentinvention have been described and illustrated, it should be noted thatthe invention is not limited thereto since modifications may be made bypersons skilled in the art. The present application contemplates any andall modifications within the spirit and scope of the underlyinginvention disclosed and claimed herein.

What is claimed is:
 1. A method for reducing timing jitter intransmission of Return-to-Zero modulated pulses comprising the steps of:measuring a total dispersion of a transmission fiber link; computing anoptimal amount of pre-chirp to be added at an input of said transmissionfiber link, wherein the optimal amount of pre-chirp to be added to theinput of the transmission fiber is −z*_(opt)B₂, where B₂ is the totaldispersion of said transmission fiber link, and z*_(opt) denotes aportion of fiber length having dispersion pre-compensated for at thetransmitter side of the fiber link; computing an optimal amount ofpre-chirp to be added at an output of said transmission fiber link,wherein the optimal amount of pre-chirp to be added to the output of thetransmission fiber is −(1−z*_(opt))B₂; adding said optimal amount ofpre-chirp to said input of said transmission fiber link; and adding saidoptimal amount of pre-chirp to said output of said transmission fiberlink.
 2. A method for reducing timing jitter in transmission ofReturn-to-Zero modulated pulses comprising the steps of: measuring atotal dispersion of a transmission fiber link; calculating z*_(opt),where z*_(opt) denotes a portion of fiber length having dispersionpre-compensated for at the transmitter side of the fiber link; computingan optimal amount of pre-chirp to be added at an input of saidtransmission fiber link using z*_(opt) and the total dispersion of thetransmission fiber link; computing an optimal amount of pre-chirp to beadded at an output of said transmission fiber link using z*_(opt) andthe total dispersion of the transmission fiber link; adding said optimalamount of pre-chirp to said input of said transmission fiber link; andadding said optimal amount of pre-chirp to said output of saidtransmission fiber link.
 3. The method according to claim 2, wherein theoptimal amount of pre-chirp to be added to the input of the transmissionfiber is −z*_(opt)B₂, where B₂ is the total dispersion of saidtransmission fiber link.
 4. The method according to claim 2, wherein theoptimal amount of pre-chirp to be added to the output of thetransmission fiber is −(1−z*_(opt)B₂, where B₂ is the total dispersionof said transmission fiber link.
 5. A method for reducing amplitudejitter in transmission of Return-to-Zero modulated phase coherent pulsescomprising the steps of: measuring a total dispersion of a transmissionfiber link; computing an optimal amount of pre-chirp to be added at aninput of said transmission fiber link, wherein said optimal amount ofpre-chirp is obtained by determining the minimum of I₂ whereI₂ = ∫₀^(L)z  f  (z)² − ∫_(−z^(*))^(L − z^(*))z  f_(w)(z + z^(*))f_(w)(−z + z^(*)),

where I₂ represents amplititude jitter, z represents fiber link length,and z* a portion of fiber length having dispersion pre-compensated forat the transmitter side of the fiber link; computing an optimal amountof pre-chirp to be added at an output of said transmission fiber link;adding said optimal amount of pre-chirp to said input of saidtransmission fiber link; and adding said optimal amount of pre-chirp tosaid output of said transmission fiber link.
 6. A system for reducingtiming jitter in transmission of Return-to-Zero modulated pulsescomprising: means for measuring a total dispersion of a transmissionfiber link; means for computing an optimal amount of pre-chirp to beadded at an input of said transmission fiber link, wherein the optimalamount of pre-chirp to be added to the input of the transmission fiberis −z*_(opt)B₂, where B₂ is the total dispersion of said transmissionfiber link, and z*_(opt) denotes a portion of fiber length havingdispersion pre-compensated for at the transmitter side of the fiberlink; means for computing an optimal amount of pre-chirp to be added atan output of said transmission fiber link, wherein the optimal amount ofpre-chirp to be added to the output of the transmission fiber is−(1−z*_(opt))B₂; means for adding said optimal amount of pre-chirp tosaid input of said transmission fiber link; and means for adding saidoptimal amount of pre-chirp to said output of said transmission fiberlink.
 7. A system for reducing timing jitter in transmission ofReturn-to-Zero modulated pulses comprising: means for measuring a totaldispersion of a transmission fiber link; means for calculating z*_(opt),where z*_(opt) denotes a portion of fiber length having dispersionpre-compensated for at the transmitter side of the fiber link; means forcomputing an optimal amount of pre-chirp to be added at an input of saidtransmission fiber link using z*_(opt) and the total dispersion of thetransmission fiber link; means for computing an optimal amount ofpre-chirp to be added at an output of said transmission fiber link usingz*_(opt) and the total dispersion of the transmission fiber link; meansfor adding said optimal amount of pre-chirp to said input of saidtransmission fiber link; and means for adding said optimal amount ofpre-chirp to said output of said transmission fiber link.
 8. The systemaccording to claim 7, wherein the optimal amount of pre-chirp to beadded to the input of the transmission fiber is −z*_(opt)B₂ , where B₂is the total dispersion of said transmission fiber link.
 9. The systemaccording to claim 7, wherein the optimal amount of pre-chirp to beadded to the output of the transmission fiber is −(1−z*_(opt))B₂, whereB₂ is the total dispersion of said transmission fiber link.
 10. A systemfor reducing amplitude jitter in transmission of Return-to-Zeromodulated phase coherent pulses comprising: means for measuring a totaldispersion of a transmission fiber link; means for computing an optimalamount of pre-chirp to be added at an input of said transmission fiberlink, wherein said optimal amount of pre-chirp is obtained bydetermining the minimum of I₂, whereI₂ = ∫₀^(L)z  f  (z)² − ∫_(−z^(*))^(L − z^(*))z  f_(w)(z + z^(*))f_(w)(−z + z^(*)),

where I₂ represents amplititude jitter, z represents fiber link length,and z* a portion of fiber length having dispersion pre-compensated forat the transmitter side of the fiber link; means for computing anoptimal amount of pre-chirp to be added at an output of saidtransmission fiber link; means for adding said optimal amount ofpre-chirp to said input of said transmission fiber link; and means foradding said optimal amount of pre-chirp to said output of saidtransmission fiber link.
 11. A system for reducing timing jitter intransmission of Return-to-Zero modulated pulses comprising: means formeasuring a total dispersion of a transmission fiber link; means forcomputing an optimal amount of pre-chirp to be added at an input of saidtransmission fiber link, wherein the optimal amount of pre-chirp to beadded to the input of the transmission fiber is −z*_(opt)B₂, where B₂ isthe total dispersion of said transmission fiber link, and z*_(opt)denotes a portion of fiber length having dispersion pre-compensated forat the transmitter side of the fiber link; means for computing anoptimal amount of pre-chirp to be added at an output of saidtransmission fiber link, wherein the optimal amount of pre-chirp to beadded to the output of the transmission fiber is −(1−z*_(opt))B₂; adispersion compensating device for adding said optimal amount ofpre-chirp to said input of said transmission fiber link; and adispersion compensating device for adding said optimal amount ofpre-chirp to said output of said transmission fiber link.
 12. A systemfor reducing timing jitter in transmission of Return-to-Zero modulatedpulses comprising: a device for measuring a total dispersion of atransmission fiber link; a computing device for calculating an optimalamount of pre-chirp to be added at an input of said transmission fiberlink, wherein the optimal amount of pre-chirp to be added to the inputof the transmission fiber is −z*_(opt) B₂, where B₂ is the totaldispersion of said transmission fiber link, and z*_(opt) denotes aportion of fiber length having dispersion pre-compensated for at thetransmitter side of the fiber link; a computing device for calculatingan optimal amount of pre-chirp to be added at an output of saidtransmission fiber link, wherein the optimal amount of pre-chirp to beadded to the output of the transmission fiber is −(1−z*_(opt))B₂; adispersion compensating device for adding said optimal amount ofpre-chirp to said input of said transmission fiber link; and adispersion compensating device for adding said optimal amount ofpre-chirp to said output of said transmission fiber link.